The classic treatise of G. Pólya, G. Szegö, [1]}, displays a wealth of isoperimetric inequalities involving quantities such as the principal eigenvalue of the Dirichlet Laplacian, moment of inertia, capacity, perimeter etc. Many of the inequalities involve just two quantities like torsional rigidity and measure (de Saint Venant's inequality, (REF ) below), principal Dirichlet eigenvalue and measure (Rayleigh Faber Krahn inequality), torsional rigidity and principal Dirichlet eigenvalue (Kohler-Jobin inequality). In each of these inequalities the ball is optimal, and their stability has been investigated in depth. See for example [2]}, and the references therein.
Examples of inequalities involving three quantities are numerous too. In this case it is convenient to display the various inequalities in a Blaschke-Santalò diagram. See for example [3]} and [4]} for torsional rigidity, principal Dirichlet eigenvalue and measure, and [5]} for perimeter, principal Dirichlet eigenvalue, and measure.
